After perusing some more ebay listings, I actually found another listing with a script J on a tie clip that looked very similar. Then after some more digging on google, I think it is this style that is closest:
Even though it looks like a G, I'd like to believe it's meant to be a J. I went ahead and purchased it in honor of my late dog that passed some years ago. Her name started with a J.
Nice find @Rubymal! You're right, it could very well be a J. I love signet rings. This one looks so pretty. And what a lovely tribute to your beloved dog. I hope you post pics when you get it!